Year :
1989
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
31 - 40 of 45 Questions
| # | Question | Ans |
|---|---|---|
| 31. |
If x : y = 5 : 12 and z = 52cm, find the perimeter of the triangle. A. 68cm B. 84cm C. 100cm D. 120cm Detailed Solution13 = 521 = \(\frac{52}{13}\) = 4 5 + 12 + 13 = 30 Total perimeter = 30 x 4 = 120cm |
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| 32. |
The pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have angles of depression of 35o and 55o. Find the distance between the two points of observation A. 10(sin 35o - sin 55o) B. 10 cos35o - cos 55o C. 10(tan35o - tan55o) D. 10(cot35o - cot55o) Detailed Solutionx = 10 cot35o - 10 cot55o= 10(cot35o - cot55o) |
|
| 33. |
4sin2 x - 3 = 0, find x if 0 \(\geq\) x \(\geq\) 90o A. 30o B. 45o C. 60o D. 9o Detailed Solution4 sin2x - 3 = 0sin2x = \(\frac{3}{4}\) Sin x = \(\pm\) \(\sqrt{\frac{3}{4}}\) = \(\pm\) \(\sqrt{\frac{3}{4}}\) = 60o |
|
| 34. |
A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m? A. 336 B. 420 C. 576 D. 720 Detailed SolutionTotal floor area = 720 x 420Area of one tile = 30 x 30 No. of tile required = \(\frac{720 \times 420}{30 \times 30}\) = 24 x 14 = 336 tiles |
|
| 35. |
A cylindrical metal pipe 1m long has an outer diameter of 7.2cm and an inner diameter of 2.8cm. Find the volume of metal used for the cylinder A. 440\(\pi\)cm3 B. 1100\(\pi\)cm3 C. 4400\(\pi\)cm3 D. 1100\(\pi\)cm3 Detailed SolutionVolume of cylinder pip (V) = \(\pi\)h(R\(^2\) - r\(^2\))= 100\(\pi\)(7.2\(^2\) - 2.8\(^2\)) = 100\(\pi\)(51.84 - 7.84) = 100\(\pi\) x 44 = 440\(\pi\)cm\(^3\) |
|
| 36. |
OXYZW is a pyramid with a square base such that OX = OY= OZ = OW = 5cm and XY = XW = YZ = WZ = 6cm. Find the height OT A. 2\(\sqrt{5}\) B. 3 C. 4 D. 4\(\sqrt{3}\) Detailed Solutionxz2 = 62 + 6236 + 36 = 72 xz = \(\sqrt{72}\) 6\(\sqrt{2}\) = xT \(\frac{6\sqrt{2}}{2}\) = \(\frac{3}{\sqrt{2}}\) OT2 = 52 + (3\(\sqrt{2}\))2 = 25 + 18 OT = 4\(\sqrt{3}\) |
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| 37. |
In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represents meat in pie chart A. 30o B. 60o C. 112.5o D. 157.5o Detailed SolutionRice = 75g, Margarine = 40g, Meat = 105g, Bread = 20g, Total = 240Angle of sector represented by meat = \(\frac{105}{240}\) x \(\frac{360°}{1}\) = 157.5° |
|
| 38. |
In a family of 21 people, the average age is 14years. If the age of the grandfather is not counted, the average age drops to 12 years. What is the age of the grandfather? A. 35 years B. 40 years C. 42 years D. 54 years Detailed SolutionTotal age of the whole family = 21 x 14 = 294Total age without the grandfather = 21 x 12 = 252 Age of grandfather = 294 - 252 = 42 years |
|
| 39. |
If n is the median and m is the mode of the following set of numbers, 2.4, 2.1, 1.6, 2.6, 2.6, 3.7, 2.1, 2.6, then (n, m) is A. (2.6, 2.6) B. (2.5, 2.6) C. (2.6, 2.5) D. (2.5, 2.1) Detailed SolutionArrange the numbers in order, 1.6, 2.1, 2.1| 2.4, 2.6| 2.6, 2.6, 3.7n = median = \(\frac{2.4 + 2.6}{2}\) = 2.5 m = mode = 2.6 ∴ (n, m) = (2.5, 2.6) |
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| 40. |
 On the curve, the points at which the gradient of the curve is equal to zero are A. i, l B. b, e, g, j, m C. a, b, c, d, f, i, j, l D. c, d, f, h, i, l Detailed SolutionThe gradient of any curve is equal to zero at the turning points. i.e. maximum or minimum points. The points in the above curve are b, e, g, j, m |
| 31. |
If x : y = 5 : 12 and z = 52cm, find the perimeter of the triangle. A. 68cm B. 84cm C. 100cm D. 120cm Detailed Solution13 = 521 = \(\frac{52}{13}\) = 4 5 + 12 + 13 = 30 Total perimeter = 30 x 4 = 120cm |
|
| 32. |
The pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have angles of depression of 35o and 55o. Find the distance between the two points of observation A. 10(sin 35o - sin 55o) B. 10 cos35o - cos 55o C. 10(tan35o - tan55o) D. 10(cot35o - cot55o) Detailed Solutionx = 10 cot35o - 10 cot55o= 10(cot35o - cot55o) |
|
| 33. |
4sin2 x - 3 = 0, find x if 0 \(\geq\) x \(\geq\) 90o A. 30o B. 45o C. 60o D. 9o Detailed Solution4 sin2x - 3 = 0sin2x = \(\frac{3}{4}\) Sin x = \(\pm\) \(\sqrt{\frac{3}{4}}\) = \(\pm\) \(\sqrt{\frac{3}{4}}\) = 60o |
|
| 34. |
A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m? A. 336 B. 420 C. 576 D. 720 Detailed SolutionTotal floor area = 720 x 420Area of one tile = 30 x 30 No. of tile required = \(\frac{720 \times 420}{30 \times 30}\) = 24 x 14 = 336 tiles |
|
| 35. |
A cylindrical metal pipe 1m long has an outer diameter of 7.2cm and an inner diameter of 2.8cm. Find the volume of metal used for the cylinder A. 440\(\pi\)cm3 B. 1100\(\pi\)cm3 C. 4400\(\pi\)cm3 D. 1100\(\pi\)cm3 Detailed SolutionVolume of cylinder pip (V) = \(\pi\)h(R\(^2\) - r\(^2\))= 100\(\pi\)(7.2\(^2\) - 2.8\(^2\)) = 100\(\pi\)(51.84 - 7.84) = 100\(\pi\) x 44 = 440\(\pi\)cm\(^3\) |
| 36. |
OXYZW is a pyramid with a square base such that OX = OY= OZ = OW = 5cm and XY = XW = YZ = WZ = 6cm. Find the height OT A. 2\(\sqrt{5}\) B. 3 C. 4 D. 4\(\sqrt{3}\) Detailed Solutionxz2 = 62 + 6236 + 36 = 72 xz = \(\sqrt{72}\) 6\(\sqrt{2}\) = xT \(\frac{6\sqrt{2}}{2}\) = \(\frac{3}{\sqrt{2}}\) OT2 = 52 + (3\(\sqrt{2}\))2 = 25 + 18 OT = 4\(\sqrt{3}\) |
|
| 37. |
In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represents meat in pie chart A. 30o B. 60o C. 112.5o D. 157.5o Detailed SolutionRice = 75g, Margarine = 40g, Meat = 105g, Bread = 20g, Total = 240Angle of sector represented by meat = \(\frac{105}{240}\) x \(\frac{360°}{1}\) = 157.5° |
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| 38. |
In a family of 21 people, the average age is 14years. If the age of the grandfather is not counted, the average age drops to 12 years. What is the age of the grandfather? A. 35 years B. 40 years C. 42 years D. 54 years Detailed SolutionTotal age of the whole family = 21 x 14 = 294Total age without the grandfather = 21 x 12 = 252 Age of grandfather = 294 - 252 = 42 years |
|
| 39. |
If n is the median and m is the mode of the following set of numbers, 2.4, 2.1, 1.6, 2.6, 2.6, 3.7, 2.1, 2.6, then (n, m) is A. (2.6, 2.6) B. (2.5, 2.6) C. (2.6, 2.5) D. (2.5, 2.1) Detailed SolutionArrange the numbers in order, 1.6, 2.1, 2.1| 2.4, 2.6| 2.6, 2.6, 3.7n = median = \(\frac{2.4 + 2.6}{2}\) = 2.5 m = mode = 2.6 ∴ (n, m) = (2.5, 2.6) |
|
| 40. |
On the curve, the points at which the gradient of the curve is equal to zero are A. i, l B. b, e, g, j, m C. a, b, c, d, f, i, j, l D. c, d, f, h, i, l Detailed SolutionThe gradient of any curve is equal to zero at the turning points. i.e. maximum or minimum points. The points in the above curve are b, e, g, j, m |